{ccc}{8}&{-1}&{9}{3}&{1}&{8}{11}&{0}&{17} eching

$$\left( \begin{array} { c c c } { 8 } & { - 1 } & { 9 } \\ { 3 } & { 1 } & { 8 } \\ { 11 } & { 0 } & { 17 } \end{array} \right)$$

Determinantni hisoblash

$$0$$

Sarrus qoidasidan foydalanish qadamlari

Diagonal usulidan foydalanib matritsaning aniqlovchisini topish.

$$det(\left(\begin{matrix}8&-1&9\\3&1&8\\11&0&17\end{matrix}\right))$$

Birinchi ikki ustunni to'rtinchi va beshinchi ustun sifatida qaytarish uchun asl matritsani kengaytirish.

$$\left(\begin{matrix}8&-1&9&8&-1\\3&1&8&3&1\\11&0&17&11&0\end{matrix}\right)$$

Pastki chap kiritmadan boshlab diagonal kamayish tarafga ko'paytirish ha koʻpaytmalarni qo'shish.

$$8\times 17-8\times 11=48$$

Pastki chap kiritmadan boshlab diagonal ko'payish tarafga koʻpaytirish va koʻpaytmalarni qoʻshish.

$$11\times 9+17\times 3\left(-1\right)=48$$

Kamayib boruvchi diagonal koʻpaytmalarning yig'indisidan ko'payib boruvchi diagonal koʻpaytmalar yig'indisini ayirish.

$$48-48$$

48 dan 48 ni ayirish.

$$0$$

Ikkilamchilar bilan kengayishdan foydalanish qadamlari

Kichik a'zolarni kengaytirish usulidan foydalanib matritsaning aniqlovchisini topish (ko'paytiruvchilarni kengaytirish deb ham nomlanadi).

$$det(\left(\begin{matrix}8&-1&9\\3&1&8\\11&0&17\end{matrix}\right))$$

Kichik a’zolarga kengaytirish uchun birinchi satrning har bir elementini o‘zining kichik a’zosiga ko‘paytiring, qaysiki ana shu elementga ega bo‘lgan satr va ustunni yo‘q qilish orqali yaratilgan 2\times 2 matritsasining maxraji hisoblanadi, so‘ngra elementning joylashuv belgisiga ko‘paytiring.

$$8det(\left(\begin{matrix}1&8\\0&17\end{matrix}\right))-\left(-det(\left(\begin{matrix}3&8\\11&17\end{matrix}\right))\right)+9det(\left(\begin{matrix}3&1\\11&0\end{matrix}\right))$$

\left(\begin{matrix}a&b\\c&d\end{matrix}\right) 2\times 2 matritsasi uchun, determinant ad-bc.

$$8\times 17-\left(-\left(3\times 17-11\times 8\right)\right)+9\left(-11\right)$$

Qisqartirish.

$$8\times 17-\left(-\left(-37\right)\right)+9\left(-11\right)$$

Yakuniy natija olish uchun shartlarni qo'shish.

$$0$$

Baholash

$$\left(\begin{matrix}8&-1&9\\3&1&8\\11&0&17\end{matrix}\right)$$